On a class of quasilinear partial integrodifferential equations with singular kernels
TLDR
In this paper, the authors prove local and global existence theorems for a model equation in nonlinear viscoelasticity, where the memory function has a singularity.About:
This article is published in Journal of Differential Equations.The article was published on 1984-04-01 and is currently open access. It has received 33 citations till now. The article focuses on the topics: Independent equation & Differential equation.read more
Citations
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Journal ArticleDOI
The Cauchy problem in one-dimensional nonlinear viscoelasticity
William J. Hrusa,J.A Nohel +1 more
TL;DR: In this paper, the authors studied the initial value problem for a nonlinear hyperbolic Volterra equation which models the motion of an unbounded viscoelastic bar and established the existence of a unique, globally defined, classical solution provided the initial data are sufficiently smooth and small.
Journal ArticleDOI
Asymptotic behavior for a viscoelastic problem with not necessarily decreasing kernel
TL;DR: A problem which arises in viscoelasticity is considered and an exponential decay of solutions under weaker assumptions than the ones frequently used in the literature is proved.
Journal ArticleDOI
Space–time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains
TL;DR: The spectral method for the partial integro-differential equations with a weakly singular kernel on irregular domains based on the nodal spectral element method using the Lagrange polynomials basis associated with the Gauss–Lobatto–Legendre quadrature nodes is proposed.
Journal ArticleDOI
Weak solutions of a class of quasilinear hyperbolic integro-differential equations describing viscoelastic materials
TL;DR: In this paper, weak solutions of scalar second-order quasilinear hyperbolic integro-differential equations with singular kernels are constructed, and conditions for the asymptotic stability of rest states are given.
Proceedings ArticleDOI
Optimal models of fractional integrators and application to systems with fading memory
TL;DR: Dynamic input-output models of fractional integrators are presented, based on simple diffusion equations, which offer many advantages, namely nonheredity and easy and efficient numerical approximation possibilities via standard methods.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Book
Bounded Analytic Functions
TL;DR: In this article, the Corona construction was used to construct Douglas algebra and interpolating sequences and Maximal Ideals were used to solve a set of problems in the Corona Construction.
Journal ArticleDOI
A Theory of the Linear Viscoelastic Properties of Dilute Solutions of Coiling Polymers
TL;DR: In this paper, the necessary coordination of the motions of different parts of a polymer molecule is made the basis of a theory of the linear viscoelastic properties of dilute solutions of coiling polymers.
Journal ArticleDOI
Dynamics of Polymer Molecules in Dilute Solution: Viscoelasticity, Flow Birefringence and Dielectric Loss
TL;DR: In this paper, the authors considered the problem of diffusing a chain molecule diffusing in a viscous fluid under the influence of external forces or currents, and calculated the viscosity, birefringence of flow, and dielectric and tensile relaxation behavior explicitly.
Journal ArticleDOI
Dynamics of concentrated polymer systems. Part 1.—Brownian motion in the equilibrium state
Masao Doi,Sam F. Edwards +1 more
TL;DR: In this paper, a mathematical model chain which describes the motion of the polymer in the fully entangled state is presented and its Brownian motion in equilibrium is studied, which shows much qualitatively different behaviour from that of the Rouse chain used in dilute solution theory.